Reverse geocoding question

Hello everyone, so I am working on a project that has me scratching my head a lot.
I want to incorporate reverse geocoding into a web page.
The web page displays seismic events, but it only shows latitude and longitude, now, I want to add a closest city and distance to said city to each latitude and longitude pair in the HTML table.
A snipet of the code follows, has anyone got any suggestions for which service to maybe try and use, it should be free preferably as I don't have funds to pay for api and so on, I don't plan on doing more than 1000 calls a day at the worsed.
Anyway the code:

                    newrow.insertCell(1).innerHTML = events.dateStr(event.ot);
                    newrow.insertCell(2).innerHTML = event.lat;
                    newrow.insertCell(3).innerHTML = event.lon;

I was thinking a service with a nice api where I can just say e.g:
lat=event.lat+long=event.long
Any help would be appreciated?
PS: The table of events gets filled, this is just the main file that is empty.

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